I downloaded a backup of our Jira-Cloud instance to restore on a locally hosted development machine, as we're migrating from one license to the other.
Simply pointing the utility at the zip file downloaded from atlassian.net yields that error.
The file is indeed a zip archive:
root@devops-jira-dl1 /var/atlassian/application-data/jira/import
$ file jira-cloud_2017-04-06.zip
jira-cloud_2017-04-06.zip: Zip archive data, at least v2.0 to extract

What's the problem?